As far as I'm aware, the mainstream religions (Catholic, Anglican, Lutheran, Orthodox, etc) agree that animals don't go to heaven. Not sure what that says about the presence of a soul though.
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Mark HendersonAug 24 '11 at 0:54

Alcorn also claims that particular animals (e.g. pets) might go to Heaven, but that would be two questions...
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El'endia Starman♦Aug 24 '11 at 0:56

1

This is heavily bound up in the definition of a "soul". Many consider having a soul quite distinct from having a spirit or, that is, having a soul which carries the image of God via the breath received by Adam and therefore being a spiritual being. Having a soul in it's most basic form may be nothing more than the ability to form relationships and bonds.
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Lawrence DolAug 24 '11 at 2:47

There's a whole spiral of questions here: if animals are created by God and are incapable of sin, why would they not be allowed into heaven? I'm not aware of any commentary about this in the Bible because I don't think it is a question which would have even occurred to the Biblical writers. (Which gets into questions about Biblical authorship… and down and down it spirals…)
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TJ LuomaOct 12 '11 at 5:21

4 Answers
4

In the Bible, the word for "spirit" is the same as "breathe." But there is ultimately a difference between the life of humans and the life in animals.

In Genesis 2:7, God breathes into the nostrils of man and gives him life, but all land animals have this same breath as well. "And they went in unto Noah into the ark, two and two of all flesh, wherein is the breath of life." (Genesis 7:15 (KJV))

However, the distinction between the two types of spirits is apparent in the following verses:

Nevertheless man being in honour abideth not: he is like the beasts
that perish.This their way is their folly: yet their posterity approve
their sayings. Selah.Like sheep they are laid in the grave; death
shall feed on them; and the upright shall have dominion over them in
the morning; and their beauty shall consume in the grave from their
dwelling. But God will redeem my soul from the power of the grave: for
he shall receive me. Selah.
Psa 49:12-15 (KJV)

Who knoweth the spirit of man that goeth upward, and the spirit of the beast that goeth downward to the earth?
Ecc. 3:21 (KJV)

It is clear that God does care for the animals. In many passages, God shows compassion for the beast or bird, whether by the law, or other means. Though they do not have eternal souls, they are part of God's creation, and they give Him His due worship.

I think the fundamental difference between the animals and humans is not the soul, but the presence of a spirit. I think that distinction can be derived from Genesis 1 (KJV):

24And God said, "Let the earth bring forth living creatures according
to their kinds—livestock and creeping things and beasts of the earth
according to their kinds." And it was so. 25And God made the beasts of
the earth according to their kinds and the livestock according to
their kinds, and everything that creeps on the ground according to its
kind. And God saw that it was good.

26Then God said, "Let us make man in our image, after our likeness.
And let them have dominion over the fish of the sea and over the birds
of the heavens and over the livestock and over all the earth and over
every creeping thing that creeps on the earth."

27So God created man in his own image, in the image of God he
created him; male and female he created them.

In verses 24-25, God describes his creation of the animals...that he made the animals "according to their kind". In verses 26-27, God describes his creation of man, and clearly delineates that man was made after HIS OWN IMAGE AND LIKENESS. The likeness of God is that of an eternal being with a spirit, the Holy Spirit.

Now may the God of peace himself sanctify you completely, and may your
whole spirit and soul and body be kept blameless at the coming of our
Lord Jesus Christ.

Where the spirit is described separately from the soul. The spirit is also described in 1 Corinthians 2 (KJV):

12Now we have received, not the spirit of the world, but the Spirit
who is from God, so that we may know the things freely given to us by
God, 13 which things we also speak, not in words taught by human wisdom,
but in those taught by the Spirit, combining spiritual thoughts with
spiritual words. 14But a natural man does not accept the things of
the Spirit of God, for they are foolishness to him; and he cannot
understand them, because they are spiritually appraised. 15But he who
is spiritual appraises all things, yet he himself is appraised by no
one.

Which brings clarity to the purpose of a healthy, living spirit... It is the spirit that is rejuvenated or given to us when we are born again. It is our spirit that gives us the ability to commune with God via his Holy Spirit. It is the part of our being that, because it is in the likeness of God, allows us to commune with him. There are differences between different translations of the bible, and some seem to indicate that unsaved man does not have a spirit, while saved man does. I am unsure what that means, or which translations are accurate. However it is an intriguing state, one which may beg the question...are we no better than animals until we accept salvation from God? Are we simply more intelligent beings with a soul until the day we repent of our sins and ask God for forgiveness and eternal life in heaven? I am not educated in the word or its language roots enough to answer that question myself, so hopefully someone more versed than I am will come along and provide a more definitive answer.

Regarding animals, there is no reference to them having a spirit in the bible. It is intriguing to note, however, that animals are referenced at least once in Revelation (that I can think of):

And the armies which were in heaven followed him upon white horses,
clothed in fine linen, white and clean.

I do believe God cared for the animals, despite the difference between them and man. He gave mankind, the beings he created in his own image and likeness, his most cherished creation, dominion over the animals and the earth, so he must have cared for the animals. I cannot say for sure what the passage from revelation means, however it seems that there will be animals in heaven as well. Whether they are the resurrected/eternal souls of animals on earth, or new creations, I cannot say.

"Regarding animals, there is no reference to them having a spirit in the bible." - No, Eccl. 3:21 takes as an assumption that animals have spirits (though the sentence itself is an uncertainty about their properties as compared to human spirits).
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Muke TeverFeb 8 '12 at 14:16

Any Biblical support? Yes; the writer of Ecclesiastes takes it as a given (Ecclesiastes 3:21, ESV quoted):

Who knows whether the spirit of man goes upward and the spirit of the beast goes down into the earth?

Also, the book of Revelation appears to refer to creatures in the sea as living souls - some translations do say living things, but the Greek word is ψυχή "breath, soul, spirit" (Revelation 16:3, KJV quoted):

And the second angel poured out his vial upon the sea; and it became as the blood of a dead man: and every living soul died in the sea.

Either way, if animals do have souls, your author is right that they may differ in important ways from human souls.

What effect are you trying to observe when you ask whether animals have souls? Or what properties associated with the English word "soul" are you looking to find in animals? A better directed question will help quell the quibbles about definitions appearing in every other answer here.

Hebrews 4:12 indicates that the word of God is able to divide the soul and the spirit. From the Bible, we understand that humans are, if I may use the word, little "trinities". We have 1) a body, 2) a soul, and 3) a spirit. This is part of the way in which mankind is made "in the image of God."

It is the spiritual part of us that distinguishes us from the animals, so animals would only have a body and a soul, with the soul being the personality.

Lastly, plants are distinguished from animals, I believe, in that there is no soul. They only have the physical aspect of existence--the body.

Some of the information contained in this post requires additional references. Please edit to add citations to reliable sources that support the assertions made here. Unsourced material may be disputed or deleted.

The trinity is not three parts of a whole, in the same way that body, soul, and spirit make up a human. So I think that analogy is inappropriate. Also, the distinction between plant and animal is not the existence or absence of a soul, but their cellular structure and metabolism.. Many microscopic animals I suspect do not have 'souls' in any meaningful way.
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FlimzyOct 10 '11 at 21:14

If you were not a regular user, I might have deleted this answer right away. However, I'll give you a chance to edit and improve it to include references and/or sources.
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El'endia Starman♦Jul 3 '14 at 20:25